Решение:
$$\frac{6}{5} - \frac{3}{4} = \frac{6 \cdot 4 - 3 \cdot 5}{5 \cdot 4} = \frac{24 - 15}{20} = \frac{9}{20}$$
$$(\frac{6}{5} - \frac{3}{4}) \cdot \frac{2}{3} = \frac{9}{20} \cdot \frac{2}{3} = \frac{9 \cdot 2}{20 \cdot 3} = \frac{18}{60} = \frac{3}{10}$$
Ответ: $$\frac{3}{10}$$